Answers
Answer:
[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]
Step-by-step explanation:
Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:
1) [tex]t = 2-x[/tex] Given
2) [tex]y = 5\cdot x +11[/tex] Given
3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties
4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property
5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property
6) [tex]y = -5\cdot (-x)+11[/tex] [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]
7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property
8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse
9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties
10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property
11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]
12) [tex]y = (-5)\cdot t +21[/tex] By 1)
13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result
14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition
15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition
16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property
17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property
18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].
Related Questions
In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 6, 6, 7, 10, 14.
Answers
Answer
The mean is 8.6
The median is 7
And the mode is 6
How long will it take for a lump-sum investment to double in value at an interest rate of 1.5% per month, compounded continuously
Answers
Answer:
It will take 47 months ( 3 years and 11 months)
Step-by-step explanation:
We use the compound interest formula here.
Mathematically;
A = P( 1 + r)^t
Where A is the amount which is 2 times the principal here, so we can call it 2P
P is the lump-sum invested
r is the monthly interest rate given as 1.5% = 1.5/100 = 0.015
t = time , which we want to calculate
Substituting these values, we have;
2P = P(1 + 0.015)^t
divide both sides by P
2 = 1.015^t
Take the log of both sides;
log 2 = log (1.015)^t
log 2 = t log 1.015
t = log2/log1.015
t = 46.55
which is approximately 47 months
Which of the following best represents the average rate at which the human hair grows?
Answers
Answer:
1/2 inch per month
Step-by-step explanation:
The average rate hair grows is about half an inch per month which is 6 inches per year.
marc mixes blue and yelow paint to ,ake green he has 14 cans blue 20 cans of yellow . he wants green color so one day 1 he mixes 4 blue 6 yellow day 2 he mixes 6 can blue 9 yellowwhats the highest number of cans each color marc can mix to mzke the same shade of green on day 3
Answers
Answer:
2 c an of blue and 5 can of yellow
Step-by-step explanation:
What number should both sides of the following equation be multiplied by to solve for g? g divided by 2 = 4
Answers
Answer: Multiply both sides by 2.
Step-by-step explanation:
g divided by 2 is equal to 4 .
We could represent that with the equation :
[tex]\frac{g}{2} = 4[/tex] To solve for g in this case multiply both sides by 2.
[tex]\frac{g}{2} * 2 = 4(2)[/tex] 2 cancels out on the left side so we will be left with g. On the right side will be left with 8 after multiplying.
g = 8
Convert the following:
4 quarts is equivalent to
ao liters (rounded to the hundredth)
Answers
Answer: 3.79 litres
Step-by-step explanation:
1 litre is equivalent to about 1.05668821 American quarts.
4 quarts would therefore be;
= 4/1.05668821
= 3.78541178
= 3.79 litres
Evaluate the expression for q = -2. 8q=
Answers
Answer:
-16
Step-by-step explanation:
8q
Let q = -2
8*-2
-16
Which of the functions below could have created this graph?
O A. F(x) = -x' +5x° +7
O B. F(x) = 2x2 - 4x2 +4
O C. F(x)=x2+x+3
O D. F(x) = -5x – 2x+5
Answers
Answer:
[tex] \boxed{f(x) = 2 {x}^{9} - 4 {x}^{2} + 4}[/tex]
Option B is the correct option
Step-by-step explanation:
By looking at the end behavior , we can say that the degree of the polynomial must be odd and leading coefficient will be positive.
Thus , the correct choice is B.
Hope I helped!
Best regards!
The polynomial function that could have created the given curve on the xy-plane is [tex]f(x)= 2x^9-4x^2+4[/tex]
What are polynomial function?Polynomial functions aree function having a leading degrees of 3 and greater.
The nature of the curve on the xy-plane depends on its end behaviour. From the given graph, the end behaviour shows that the equivalnt function has a positive leading coefficient and an odd degree.
From the listed option, the function that satisfies both criteria is [tex]f(x)=2x^9-4x^2+4[/tex].
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Extensive experience with fans of a certain type used in diesel engines has suggested that the exponential distribution provides a good model for time until failure. Suppose the mean time until failure is 23,100 hours.
(a) What is the probability that a randomly selected fan will last at least 20,000 hours?
What is the probability that a randomly selected fan will last at most 30,000 hours?
What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?
(b) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?
What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?
Answers
Answer:
0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832
Step-by-step explanation:
For an exponential distribution:
IF Mean time until failure = 23100
λ = 1/ 23100 = 0.0000432900
What is the probability that a randomly selected fan will last at least 20,000 hours
x ≥ 20000
P(X ≥ 20000) = 1 - P(X ≤ 20000)
1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]
1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)
1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]
1 - P(X ≤ 20000) = 1 - 0.5792851
1 - P(X ≤ 20000) = 0.4207149
11) What is the probability that a randomly selected fan will last at most 30,000 hours?
x ≤ 30000
P(X ≤ 30000) = 1 - e^(-λx)
P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)
= 1 - e^(−1.2987)
= 1 - 0.2728863
= 0.7271136
111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?
0.7271136 - 0.4207149 = 0.3063987
B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?
More than two standard deviation
X = 23100 + 2(23100) = 23100 + 46200 = 69300
Using the online exponential probability calculator :
P(X > 69300) = 0.04979
C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?
X = 23100 + 3(23100) = 23100 + 69300 = 92400
P(X > 92400) = 0.01832
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answers
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
Algebra Review
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n^3 +9.
Answers
Answer:
Step-by-step explanation:
1. The sum of one-third of a number and 27
= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]
2. The product of a number squared and 4
[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]
3.Write a verbal expression for 5n^3 +9.
The sum of the product and of 5 and a cubed number and 9
A soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification. Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration. What is the probability that the assembly line will be shut down, given that it is actually calibrated correctly? Use Excel to find the probability. Round your answer to three decimal places.
Answers
Answer:
The probability that the assembly line will be shut down is 0.00617.
Step-by-step explanation:
We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.
Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.
Let X = Number of bottles in the sample that are not within specification.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 12 bottles
x = number of success = 2 or more bottles
p = probabilitiy of success which in our question is probability that
bottles are not within specification, i.e. p = 0.01
So, X ~ Binom (n = 12, p = 0.01)
Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)
P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)
= [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]
= [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]
= 0.00617
HELP ASAP ROCKY!!! will get branliest.
Answers
Answer:
y = 8x + 70
Step-by-step explanation:
Start with the third line.
x = 3, y = 94
Subtract 1 from x and 8 from y:
x = 2, y = 86; this is the second line
Subtract 1 from x and 8 from y:
x = 1, y = 78; this is the first line
Subtract 1 from x and 8 from y:
x = 0; y = 70
For selling 0 games, she earns $70.
y = mx + b
y = mx + 70
For each game she sells, her commission is $8.
y = 8x + 70
23.24 divided by 2.8
Answers
Answer:
It's 8.3
Step-by-step explanation:
Answer:
8.3
Step-by-step explanation:
Please answer this correctly without making mistakes
Answers
Answer:
so first convert to fraction so
9 3/4 = 39/4
so it was spread among 3
so this is division so you do 39/4 divided by 3
so you keep switch flip
which is 39/4 *1/3
answer is 13/4
Answer:
3 1/4 bagsStep-by-step explanation:
[tex]9\frac{3}{4}= \frac{(4 \times 9)+3}{4}= \frac{39}{4} \\\\\frac{39}{4} = 3 \:vegetable \: beds\\x \:\:\:= 1 \: vegetable \:bed\\\\3x = \frac{39}{4} \\\\\frac{3x}{3} = \frac{\frac{39}{4} }{3} \\\\x = \frac{13}{4} \\\\x = 3\frac{1}{4}[/tex]
identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
Answers
[tex]10[/tex] divisions between $20$ and $20.1$ so each division is $\frac{20.1-20.0}{10}=0.01$
A is 2nd division from $20.0$, so, A is $20.0+2\times 0.01=20.02$
similarly, C is one division behind $20.0$ so it is 19.99
and B is $20.14$
The lower edge of a 5 foot tall painting is 5 feet above your eye level. At what distance should you stand from the wall so your viewing angle of the painting is maximized?
Answers
Answer:
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Step-by-step explanation:
referring to the diagram
theta (x) = atan(10/x) - atan(5/x)
differentiate with respect to x
theta'(x) = 5/(x^2+25) - 10/(x^2+100)
For x to have an extremum (max. or min)
theta'(x) = 0 ="
5/(x^2+25) - 10/(x^2+100) = 0
transpose and cross multiply
10(x^2+25) -5(x^2+100) = 0
expand and simplify
10x^2+250 - 5x^2-500 = 0
5x^2 = 250
x^2=50
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Since we know that if x becomes large, theta will decrease, so
x = 5sqrt(2) is a maximum.
Express as a trinomial (3x+8) (x+10)
Answers
Answer:
[tex]3x^{2} +38x+80[/tex]
Step-by-step explanation:
Hello!
A trinomial is a expression consisting of three different terms
To turn this into a trinomial we multiply everything to each other
3x
3x * x = [tex]3x^{2}[/tex]
3x * 10 = 30x
8
8 * x = 8x
8 * 10 = 80
Now we put them all together in an equation
[tex]3x^{2} +30x+8x+80[/tex]
Combine like terms
[tex]3x^{2} +38x+80[/tex]
The answer is [tex]3x^{2} +38x+80[/tex]
Hope this helps!
Evaluate 3h(2) + 2k(3) =
Answers
Answer:
6h + 6kStep-by-step explanation:
[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]
Answer:
Answers for E-dge-nuityyy
Step-by-step explanation:
(h + k)(2) = 5
(h – k)(3) = 9
Evaluate 3h(2) + 2k(3) = 17
Suppose that the function g is defined, for all real numbers, as follows.
find g(-5) g(1) g(4)
Answers
=================================================
Explanation:
The piecewise function shows that we have two cases. Either x = 1 or [tex]x \ne 1[/tex].
If x = 1, then g(x) = 3 as shown in the bottom row. This is why g(1) = 3.
If [tex]x \ne 1[/tex], then g(x) = (1/4)x^2-4
Plug x = -5 into this second definition
g(x) = (1/4)x^2-4
g(-5) = (1/4)(-5)^2-4
g(-5) = (1/4)(25)-4
g(-5) = 25/4 - 4
g(-5) = 25/4 - 16/4
g(-5) = 9/4
Repeat for x = 4
g(x) = (1/4)x^2-4
g(4) = (1/4)(4)^2-4
g(4) = (1/4)(16)-4
g(4) = 4-4
g(4) = 0
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
g(x) = (1/4)x² - 4, x ≠ 1
g(x) = 3, x = 1
The value of the function at x = -5 will be given as,
g(-5) = (1/4)(-5)² - 4
g(-5) = 25 / 4 - 4
g(-5) = 6.25 - 4
g(-5) = 2.25
The value of the function at x = 4 will be given as,
g(4) = (1/4)(4)² - 4
g(4) = 16 / 4 - 4
g(4) = 4 - 4
g(4) = 0
The value of the function at x = 1 will be given as,
g(1) = 3
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
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A baseball player has a batting average of 0.26. What is the probability that he has exactly 6 hits in his next 7 at bats
Answers
Answer:
0.0016
Step-by-step explanation:
Batting average, p = 0.26
n = 7
x = 6
With p = 0.26 as success rate
1-p is equal to failure rate which is = 0.74
We have to solve this by using the binomial distribution formula.
P(X= x)
= nCx * p^x * (1-p)^(n-x)
P(X = 6)
=7C6 × 0.26^6 ×(1-0.26)^(7-6)
= 7 × 0.0003089 × 0..74¹
= 0.0016
So probability that he has exactly 6 hits in his next 7 bats is equal to 0.0016.
Which graph has an amplitude of 1/2?
Answers
Answer:
Step-by-step explanation:
The only graph shown in the question doesn't have amplitude 1/2. look for a graph of a periodic wave function that has maximum y-value 1/2 (0.5) and minimum y-value 1/2 (0.5), or if it is not oscillating around the x-axis, verifies that the distance between minimum y-value and maximum y-value is "1" (one). This is because the amplitude is half of the peak-to-peak distance.
Look at the attached image as example.
Answer:
Answer is B
Step-by-step explanation:
Did it on Edge
if the sin 30 = 1/2, then which statement is true?
Answers
Answer:
cos 60° = 1/2 because the angles are complements.
Step-by-step explanation:
An architect is designing a gym for a new elementary
school. The gym will be 116 feet long and have an area of
6,960 square feet. What will be the width of the gym?
Answers
The width of the gym will be W=60 feet for the area of 6,960 square feet.
What is area?Area is defines as the space covered by a surface in the two dimensional plane.
It is given that
Area of the gym =6960 square feet
Width of the gym = ?
Length of the gym=116 feet
The width of the gym will be calculated as
[tex]A=\L\times W\\\\\\6960=116\times W\\\\\\w=\dfrac{6960}{116}=60\ \ Feet[/tex]
hence the width of the gym will be W=60 feet for the area of 6,960 square feet.
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classify the following triangle
Answers
The one-sample z ‑statistic for Thomas' statistical test has a value of −1.73346 , and Thomas calculates a P-value of 0.0830 . Should Thomas conclude that telephone surveys provide adequate coverage with respect to p ? Why or why not? Select all correct statements about his decision and conclusion.
Answers
Answer:
Thomas should not reject the null hypothesis.
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. Here in this question the test value is -1.73346 and p-value is 0.0830. The p value is greater than the test value therefore the null hypothesis should be accepted.
Show that the set of functions from the positive integers to the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is uncountable. [Hint: First set up a one-to-one correspondence between the set of real numbers between 0 and 1 and a subset of these functions. Do this by associating to the real number 0.d1d2 . . . dn . . . the function f with f(n).
Answers
Answer:
since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its off functions
Step-by-step explanation:
set = {0,1,2,3,4,5,6,7,8,9}
setting up a one-to-one correspondence between the set of real numbers between 0 and 1
The function : F(n)= {0,1} is equivalent to the subset (sf) of (n) , this condition is met if n belongs to the subset (sf) when f(n) = 1
hence The power set of (n) is uncountable and is equivalent to the set of real numbers given
since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its offfunctions
Sarah knows how important it is to budget her monthly expenses. She earns $3,120 every month and her monthly expenses total to $2,130. Sarah has summarized her monthly expenses using the pie chart below. What percent of Sarah's monthly income is left over after she pays her monthly bills? Round to the dollar
Answers
Answer: 37.1%
Step-by-step explanation:
2130/3120×100% = 68.3%
100% - 68.3%
=31.7%
37.1%
which makes that $460
May I have brainliest please? :)
Also, the person above me smells like how a diaper tastes
To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8
Answers
Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
The one-sample z test is: a. a hypothesis test b. used to test hypotheses c. concerning a single population with a known variance d. concerning at least one population e. concerning the variance in a population d. all of the above
Answers
Answer:
d. all of the above
Step-by-step explanation:
A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used
